RPM to Rad/s Converter

Convert revolutions per minute (RPM) to radians per second (rad/s) for angular velocity measurements in engineering, physics, and mechanical applications. This converter provides precise conversions for rotational speed analysis.

Enter Value in Revolutions per Minute (RPM):

Decimal Precision:

Quick Reference Conversion Table

Common RPM to rad/s conversions for frequently encountered rotational speeds in motors, engines, and machinery.

RPM	rad/s	RPM	rad/s
1	0.1047	100	10.472
5	0.5236	200	20.944
10	1.0472	300	31.416
15	1.5708	500	52.360
20	2.0944	750	78.540
30	3.1416	1000	104.720
50	5.2360	1500	157.080
60	6.2832	3000	314.159
75	7.8540	5000	523.599

Conversion Formula and Method

The conversion from revolutions per minute to radians per second involves two fundamental concepts: there are 60 seconds in one minute, and one complete revolution equals 2π radians.

rad/s = RPM × (2π ÷ 60)

rad/s = RPM × 0.10472

Where π (pi) ≈ 3.14159, making the conversion factor approximately 0.10472 radians per second for each revolution per minute.

Step-by-Step Conversion Process

Identify the rotational speed value in revolutions per minute (RPM)
Multiply the RPM value by 2π (approximately 6.28318)
Divide the result by 60 to convert from per minute to per second
The final value represents the angular velocity in radians per second

Worked Example

To convert 120 RPM to rad/s:

Given: 120 RPM

Step 1: 120 × 2π = 120 × 6.28318 = 753.982

Step 2: 753.982 ÷ 60 = 12.566 rad/s

Answer: 120 RPM = 12.566 rad/s

Unit Comparison

Revolutions per Minute (RPM)

Definition: The number of complete rotations an object makes in one minute.

Common Usage: Engine speeds, fan speeds, drill speeds, centrifuges, record players

Typical Range: 0 to 20,000+ RPM depending on application

Radians per Second (rad/s)

Definition: The rate of change of angular position, measuring how many radians are traversed per second.

Common Usage: Physics equations, angular momentum, rotational kinematics, scientific calculations

Typical Range: 0 to 2,000+ rad/s in most applications

Notable Rotational Speeds

Application	Typical RPM	Equivalent rad/s
Vinyl record (33⅓ RPM)	33.33	3.49
Car engine idle	600-1000	62.8-104.7
Washing machine spin	1000-1400	104.7-146.6
Hard disc drive (HDD)	5400-7200	565.5-753.9
Car engine maximum	5000-8000	523.6-837.8
Dentist drill	300,000+	31,416+

Why Radians per Second?

Radians per second serve as the standard unit for angular velocity in scientific and engineering contexts because radians are dimensionless, simplifying mathematical relationships in physics. When angular velocity is expressed in rad/s, formulas for angular momentum, rotational kinetic energy, and centripetal acceleration become more straightforward.

The relationship between linear velocity (v) and angular velocity (ω) is given by v = r × ω, where r is the radius. This elegant relationship only holds when ω is measured in radians per second, making it the preferred unit for theoretical work.

Reverse Conversion: Rad/s to RPM

To convert from radians per second back to revolutions per minute, reverse the process by multiplying by 60 and dividing by 2π:

RPM = rad/s × (60 ÷ 2π)

RPM = rad/s × 9.5493

Frequently Asked Questions

What does RPM stand for?

RPM stands for revolutions per minute. It measures how many complete 360-degree rotations an object completes in 60 seconds. This unit is commonly displayed on tachometers in vehicles and on machinery control panels.

Why use radians instead of degrees?

Radians are the natural unit for angles in mathematics and physics because they create direct relationships between arc length, radius, and angle. One radian is the angle subtended when the arc length equals the radius, making many formulas simpler and more elegant without conversion constants.

How many radians are in one complete revolution?

One complete revolution equals 2π radians, which is approximately 6.28318 radians. This corresponds to 360 degrees. Therefore, half a revolution is π radians (180 degrees), and a quarter revolution is π/2 radians (90 degrees).

Is angular velocity the same as rotational speed?

Angular velocity and rotational speed are closely related but measured differently. Rotational speed (RPM) counts complete revolutions, whilst angular velocity (rad/s) measures the rate of change of angular position. Both describe how fast something rotates, just in different units.

Can I convert negative RPM values?

Yes, negative values indicate rotation in the opposite direction. The conversion formula works identically for negative numbers. For example, -100 RPM equals -10.472 rad/s, representing anticlockwise rotation if the positive direction is defined as clockwise.

What’s the difference between angular velocity and linear velocity?

Angular velocity (measured in rad/s or RPM) describes how fast an object rotates around an axis, whilst linear velocity (measured in m/s or mph) describes how fast a point moves through space. For a rotating object, points farther from the centre have greater linear velocity but the same angular velocity.

How precise should my conversions be?

The required precision depends on your application. For general engineering work, 3-4 decimal places typically suffice. Scientific research or high-precision machinery may require 5-6 decimal places. Always match your precision to the accuracy of your input measurements.